No expectation of privacy does not mean you can follow someone around all day and keep a log of what they do, which is essentially what this thing does.
Over the course of a days/weeks, the places one visits, roads you drive on, etc. those things should definitely be private.
Isn't that what paparazzi do already? Seems like you can do that.
Why doesn't it mean that?
Isn't that exactly what a stakeout is? Or an undercover operation?
I didn't search for undercover, but I can find nothing about a warrant being required for a stakeout in the US (and numerous results saying no warrant is required).